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Points: 25
Time limit: 2.0s
Memory limit: 64M

Problem type

There are N stones, numbered 1, 2, \ldots, N. For each i\ (1 \le i \le N), the height of Stone i is h_i. Here, h_1 < h_2 < \ldots < h_N holds.

There is a frog who is initially at Stone 1. He will repeat the following action some number of times to reach Stone N:

  • If the frog is currently on Stone i, jump to one of the following stones: Stone i+1, i+2, \ldots, N. Here, a cost of (h_j - h_i)^2 + C is incurred, where j is the stone to land on.

Find the minimum possible total cost incurred before the frog reaches Stone N.

Constraints

  • All values in input are integers.
  • 2 \le N \le 2 \times 10^5
  • 1 \le C \le 10^{12}
  • 1 \le h_1 < h_2 < \ldots < h_N \le 10^6

Input Specification

The first line will contain two integers N, C.

The second line will contain N integers, h_i.

Output Specification

Print the minimum possible total cost incurred.

Sample Input 1

5 6
1 2 3 4 5

Sample Output 1

20

Explanation For Sample 1

If we follow the path 1 \rightarrow 3 \rightarrow 5, the total cost incurred would be ((3-1)^2 + 6) + ((5-3)^2+6) = 20.

Sample Input 2

2 1000000000000
500000 1000000

Sample Output 2

1250000000000

Explanation For Sample 2

The answer may not fit into a 32-bit integer type.

Sample Input 3

8 5
1 3 4 5 10 11 12 13

Sample Output 3

62

Explanation For Sample 3

If we follow the path 1 \rightarrow 2 \rightarrow 4 \rightarrow 8, the total cost incurred would be ((3-1)^2+5) + ((5-3)^2+5) + ((10-5)^2+5) + ((13-10)^2+5) = 62.


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